Model-based QTL detection is sensitive to slight modifications in model formulation

Autoři: Caterina Barrasso aff001;  Mohamed-Mahmoud Memah aff002;  Michel Génard aff002;  Bénédicte Quilot-Turion aff001
Působiště autorů: GAFL, INRA, 84143, Montfavet, France aff001;  PSH, INRA, 84914, Avignon, France aff002
Vyšlo v časopise: PLoS ONE 14(10)
Kategorie: Research Article
doi: 10.1371/journal.pone.0222764


Classical crop models have been developed to predict crop yield and quality, and they are based on physiological and environmental inputs. After molecular discoveries, models should integrate genetic variation to allow predictions that are more genotype-dependent. An interesting approach, Quantitative Trait Locus (QTL)-based ecophysiological modeling, has shown promising results for the design of ideotypes that are adapted to biotic and abiotic stresses, but there are still limitations to attaining a fully integrated model. The aim of this case study is to clarify the impact of choosing different model equations (closely related and with different numbers of parameters) and optimization methods on the detection of QTLs controlling the parameters of crop growth. Different growth equations were parameterized based on a genetic population by following different approaches. The correlations between parameters were analyzed, and two different strategies were adopted to address the correlation issue. QTL analysis was performed on the optimized values of the parameters of the growth equations and on the observed dry mass (DM) data to validate the QTLs detected. Overall, models and strategies resulted in different QTLs being detected. Similar LOD profiles but with peaks of different heights were observed, some of which were significant, resulting in different numbers of QTLs. In some cases, peaks had slightly different positions or were absent. Even closely related growth models led to the detection of different QTLs. The goodness of fit and complexity of the growth models were found to be insufficient to select the best model. Calculating parameters independently of observed data may not be a good strategy, whereas setting parameters independent of the genotype is recommended. Given the large-scale global optimization problem and the strong correlations between parameters, the two algorithms tested showed poor performance. Currently, the lack of effective algorithms is the main obstacle to answering the question posed. The authors therefore suggest testing different model formulations and comparing the QTLs detected before choosing the best formulation to use in an ecophysiological modeling approach based on QTLs.

Klíčová slova:

Algorithms – Crop genetics – Crops – Fruits – Gene mapping – Genetic polymorphism – Population genetics – Quantitative trait loci


1. Martre P, Bertin N, Salon C, Gérard M. Modelling the size and composition of fruit, grain and seed by process-based simulation models. New phytol. 2011, 191: 601–618. doi: 10.1111/j.1469-8137.2011.03747.x 21649661

2. Boote KJ, Kropff MJ, Bindraban PS. Physiology and modelling of traits in crop plants: implications for genetic improvement. Agric Syst. 2001, 70: 395–420.

3. Tardieu F. Virtual plants: modelling as a tool for the genomics of tolerance to water deficit. Trend plant sci. 2003, 8: 9–14.

4. Yin X, Chasalow S, Dourleijn CJ, Stam P, Kropff MJ. Coupling estimated effects of QTLs for physiological traits to a crop growth model: predicting yield variation among recombinant inbred lines in barley. Heredity. 2000, 85: 539–549. doi: 10.1046/j.1365-2540.2000.00790.x 11240620

5. Bertin N, Martre P, Génard M, Quilot B, Salon C. Under what circumstances can process-based simulation models link genotype to phenotype for complex traits? case-study of fruit and grain quality traits. J Exp Bot. 2010. doi: 10.1093/jxb/erp377 20038518

6. Yin X, Kropff MJ, Stam P. The role of ecophysiological models in QTL analysis: The example of specific leaf area in barley. Heredity. 1999. doi: 10.1038/sj.hdy.6885030 10383660.

7. Yin X, Stam P, Kropff MJ, Schapendonk AHCM. Crop modeling, QTL mapping, and their complementary role in plant breeding. Agron J. 2003a, 95: 90–98.

8. Constantinescu D, Memmah MM, Vercambre G, Génard M, Baldazzi V, Causse M et al. Model-Assisted Estimation of the Genetic Variability in Physiological Parameters Related to Tomato Fruit Growth under Contrasted Water Conditions. Front Plant Sci. 2016. doi: 10.3389/fpls.2016.01841 28018381

9. Yin X, Struik PC, Gu J, Wang H. Modelling QTL-Trait-Crop Relationships: Past Experiences and Future Prospects. In: Yin X, Struik PC, editors. Crop Systems Biology. Springer; 2016. pp. 193–213.

10. Wei K, Wang J, Sang M, Zhang S, Zhou H, Jiang L, et al. An ecophysiologically based mapping model identifies a major pleiotropic QTL for leaf growth trajectories of Phaseolus vulgaris. Plant Journal 2018. Available from:

11. Wu R, Lin M. Opinion: Functional mapping—How to map and study the genetic architecture of dynamic complex traits. Nature Reviews Genetics 2006. Available from:

12. Li Y, Wu R. Functional mapping of growth and development. Biological Reviews 2010. Available from:

13. Li Q, Huang Z, Xu M, Wang C, Gai J, Huang Y, et al. Functional mapping of genotype environment interactions for soybean growth by a semiparametric approach. Plant Methods 2010. Available from:

14. Huang Z, Tong C, Bo W, Pang X, Wang Z, Xu J, et al. An allometric model for mapping seed development in plants. Briefings in Bioinformatics 2014. Available from:

15. Hou W, Li H, Zhang B, Huang M, Wu R. A non linear mixed-effect mixture model for functional mapping of dynamic traits. Heredity 2008. Available from:

16. Chang-Xing M, Casella G, Wu R. Functional mapping of quantitative trait loci underlying the character process: A theoretical framework. Genetics 2002; 161(4): 1751–1762. 12196415

17. Xing J, Li J, Yang R, Zhou X, Xu S. Bayesian B-spline mapping for dynamic quantitative traits. Genetics Research 2012. Available from:

18. Wu W, Zhou Y, Li W, Mao D, Chen Q. Mapping of quantitative trait loci based on growth models. Theoretical and Applied Genetics 2002. Available from:

19. Quilot-Turion B, Ould Sidi M, Kadrani A, Hilgert N, Génard M, Lescourret F. Optimization of genetic parameters of the 'Virtual Fruit' model to design peach ideotypes for sustainable production systems. European Journal of Agronomy 2012; 42: 34–48.

20. Podisi BK, Knott SA, Burt DW, Hocking PM. Comparative analysis of quantitative trait loci for body weight, growth rate and growth curve parameters from 3 to 72 weeks of age in female chickens of a broiler-layer cross. BMC Genetics 2013. Available from:

21. Ashyraliyev M, Fomekong-Nanfack Y, Kaandorp JA, Blom JG. Systems biology: parameter estimation for biochemical models. FEBS J. 2009. doi: 10.1111/j.1742-4658.2008.06844.x 19215296

22. Chou IC, Voit EO. Recent developments in parameter estimation and structure identification of biochemical and genomic systems. Math Biosci. 2009, 219: 57–83. doi: 10.1016/j.mbs.2009.03.002 19327372

23. Li P, Vu QD. Identification of parameter correlations for parameter estimation in dynamic biological models. BMC Syst biol. 2013, 7: 91. doi: 10.1186/1752-0509-7-91 24053643

24. Li P, Vu QD. A simple method for identifying parameter correlations in partially observed linear dynamic models. BMC Syst biol. 2015. doi: 10.1186/s12918-015-0234-3 26666642

25. Kwak IY, Moore CR, Spalding EP, Broman KW. A simple regression-based method to map quantitative trait loci underlying function-valued phenotypes. Genetics 2014. Available from:

26. Lescourret F, Génard M. A virtual peach fruit model simulating changes in fruit quality during the final stage of fruit growth. Tree Physiology 2005; 25: 1303–1315. doi: 10.1093/treephys/25.10.1303 16076779

27. Quilot B, Wu BH, Kervella J, Génard M, Foulongne M, Moreau K. QTL analysis of quality traits in an advanced backcross between Prunus persica cultivars and the wild relative species P. davidiana. Theor appl genet. 2004, 109: 884–897. doi: 10.1007/s00122-004-1703-z 15168024

28. Quilot B, Génard M, Lescourret F, Kervella J. Simulating genotypic variations of fruit quality in an advanced peach x Prunus davidiana cross. J Exp Bot. 2005, 56: 3071–3081. doi: 10.1093/jxb/eri304 16234284

29. Verhulst PF. Notice sur la loi que la population suit dans son accroissement. Correspondence Mathématiques et Physiques, 1838, 10: 113–121 (in french).

30. Gibert C, Lescourret F, Génard M, Vercambre G, Perez Pastor A. Modelling the effect of fruit growth on surface conductance to water vapour diffusion. Ann Bot. 2005, 95: 673–683. doi: 10.1093/aob/mci067 15655107

31. Lechaudel M, Génard M, Lescourret F, Urban L, Jannoyers M. Modeling effects of weather and source–sink relationships on mango fruit growth. Tree Physiol. 2005, 25: 583–597. doi: 10.1093/treephys/25.5.583 15741151

32. Grechi I, Hilgert N, Sauphanor B, Senoussi R, Lescourret F. Modelling coupled peach tree–aphid population dynamics and their control by winter pruning and nitrogen fertilization. Ecol Modell. 2010, 221: 2363–2373.

33. Yin X, Goudriaan J, Lantinga EA, Vos J, Spiertz HJ. A flexible sigmoid function of determinate growth. Ann Bot. 2003b, 91: 361–371. doi: 10.1093/aob/mcg029 12547689

34. Yin X, Goudriaan J, Lantinga EA, Vos J, Spiertz HJ. A flexible sigmoid function of determinate growth (ERRATUM). Ann Bot. 2003c, 91: 361–371. doi: 10.1093/aob/mcg029 12547689

35. Richards FJ. A flexible growth function for empirical use. J Exp Bot. 1959, 10: 290–300.

36. Gompertz B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Phil Trans. 1825, 182: 513–585.

37. Goudriaan J, Monteithf JL. A Mathematical Function for Crop Growth Based on Light Interception and Leaf Area Expansion. Ann Bot. 1990, 66: 695–701.

38. Comets E, Lavenu A, Lavielle M. Parameter Estimation in Nonlinear Mixed Effect Models Using saemix, an R Implementation of the SAEM Algorithm. Journal of Statistical Software 2017. doi: 10.18637/jss.v080.i03

39. Quilot B, Génard M, Valsesia P, Memmah MM. Optimization of allelic combinations controlling parameters of peach quality model. Front Plant Sci. 2016. doi: 10.3389/fpls.2016.01873 28066450

40. Sundararajan PK, Mengshoel OJ. A Genetic Algorithm for Learning Parameters in Bayesian Networks using Expectation Maximization. Paper presented at the Proceedings of the Eighth International Conference on Probabilistic Graphical Models, Proceedings of Machine Learning Research, 2016.

41. Lucasius CB, Kateman G. 1993. Understanding and using genetic algorithms—Part 1. Concepts, properties and context. Chemometr intel lab. 1993, 19: 1–33.

42. Lucasius CB, Kateman G. Understanding and using genetic algorithms—Part 2. Representation, configuration and hybridization. Chemometr intel lab. 1994, 25: 99–145.

43. Willighagen E. genalg: R-Based Genetic Algorithm. R package version 0.2.0. 2015. Available from:

44. Desnoues E, Baldazzi V, Génard M, Mauroux JB, Lambert P, Confolent C et al. Dynamic QTLs for sugars and enzyme activities provide an overview of genetic control of sugar metabolism during peach fruit development. J Exp Bot. 2016. doi: 10.1093/jxb/erw169 27117339

45. Haley CS, Knott SA. A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 1992; 69: 315–324. doi: 10.1038/hdy.1992.131 16718932

46. Kruglyak L, Lander ES. A nonparametric approach for mapping quantitative trait loci. Genetics 1995; 139: 1421–1428. 7768449

47. Salazar JA, Ruiz D, Campoy JA, Sánchez-Pérez R, Crisosto CH, Martínez-García PJ, Blenda A, Jung S, Main D, Martínez-Gómez P, Rubio M. Quantitative trait loci (QTL) and mendelian trait loci (MTL) analysis in Prunus: a breeding perspective and beyond. Plant Molecular Biology Reporter, 2014, 32: 1–18.

48. Cirilli M, Bassi D, Ciacciulli A. Sugars in peach fruit: a breeding perspective. Horticulture Research, 2016, 3: 15067 doi: 10.1038/hortres.2015.67 26816618

49. Ioannidis JPA, Trikalinos TA, Ntzani EE, Contopoulos-Ioannidis DG. Genetic associations in large versus small studies: an empirical assessment. Lancet. 2003. 361, 567–571. doi: 10.1016/S0140-6736(03)12516-0 12598142

50. Jian-Bing Y, Ji-Hua T, Yi-Jiang M, Xi-Qing M, Wen-Tao T, Chander S, Lin L, Jiang-Sheng L. Improving QTL Mapping Resolution Based on Genotypic Samplying-a Case using a RIL Population. Acta Genetica Sinica. 2006. 33: 617–624. doi: 10.1016/S0379-4172(06)60091-7 16875319

51. Wang M, Xu S. Statistical power in genome-wide association studies and quantitative trait locus mapping. Heredity. 2019. doi: 10.1038/s41437-019-0205-3 30858595

52. Chen S, Montgomery J, Bolufé-Röhler A. Measuring the curse of dimensionality and its effects on particle swarm optimization and differential evolution. Artif Intell. 2015. doi: 10.1016/j.artint.2014.11.008

53. Mei Y, Omidvar MN, Li X, Yao X. A Competitive Divide-and-Conquer Algorithm for Unconstrained Large-Scale Black-Box Optimization. ACM t math software. 2016. doi: 10.1145/2791291

54. Mahdavi S, Shiri ME, Rahnamayan S. Metaheuristics in large-scale global continues optimization: A survey. Inform sciences. 2015. doi: 10.1016/j.ins.2014.10.042

Článek vyšel v časopise


2019 Číslo 10